A homotopy theory for stacks
Author(s)Hollander, Sharon Joy, 1975-
Massachusetts Institute of Technology. Dept. of Mathematics.
Michael J. Hopkins.
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We give a homotopy theoretic characterization of stacks on a site C which allows one to think of stacks as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category, that is a formal homotopy theory, in which stacks play the special role of the fibrant objects. This allows us to compare the different definitions of stacks and show that they lead to Quillen equivalent model categories. In addition, these model structures are Quillen equivalent to the S2-nullification of Jardine's model structure on sheaves of simplicial sets on e.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.Includes bibliographical references (p. 69-70).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology